Estimating the Effective Reproduction Number of COVID-19 in United Kingdom
Louis Rossouw
2021-05-08 22:45:02 BST
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various nations and other regions \(m\) of United Kingdom. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was df2bbec2d38e83f3fbdb7831cf6735c960f0db5e.
2 Data
Data is obtained [3]. This contains the daily cases, hospital admissions and deaths for United Kingdom by various geographies. Here the data is accessed by specimen date, admission date and date of death.
Once history is built up an allowance for rate reported cases, admissions and deaths will be made. For now the data is cut-off a week prior to the last case date in the data. All data prior to 1 March 2020 are removed.
3 Methodology
The methodology is described in detail here.
4 Results by Nation
4.1 Cases
Below a 7-day moving average of daily case count on a log scale by nation is plotted:
Daily Cases by Nation (7-day moving average)
4.2 Admissions
Below we plot cumulative hospital admissions on a log scale.
Daily Admissions by Nation (7-day moving average)
4.3 Deaths
Below a 7-day moving average of daily deaths by nation on a log scale is plotted:
Daily Deaths by Nation (7-day moving average)
4.4 Current \(R_{t,m}\) estimates by Nation
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Nation | Estimate Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| England | cases | 1,818.7 | 2021-05-01 | 0.9 | 0.9 | 1.0 |
| England | admissions | 94.6 | 2021-05-01 | 0.8 | 0.9 | 0.9 |
| England | deaths | 9.4 | 2021-05-01 | 0.6 | 0.7 | 0.9 |
| Northern Ireland | cases | 93.4 | 2021-05-01 | 0.9 | 1.0 | 1.1 |
| Northern Ireland | admissions | 4.9 | 2021-05-01 | 0.6 | 0.9 | 1.2 |
| Northern Ireland | deaths | 0.6 | 2021-05-01 | 0.2 | 0.7 | 1.5 |
| Scotland | cases | 167.0 | 2021-05-01 | 0.8 | 0.9 | 0.9 |
| Scotland | admissions | 8.0 | 2021-05-01 | 0.6 | 0.8 | 1.0 |
| Scotland | deaths | 0.7 | 2021-05-01 | 0.3 | 0.7 | 1.4 |
| Wales | cases | 45.1 | 2021-05-01 | 0.8 | 0.9 | 1.0 |
| Wales | admissions | 14.1 | 2021-05-01 | 0.7 | 0.9 | 1.1 |
| Wales | deaths | 0.3 | 2021-05-01 | 0.1 | 0.5 | 1.3 |
Estimated Effective Reproduction Number by Nation
4.5 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [4].
4.5.1 Cases
4.5.2 Admissions
4.5.3 Deaths
4.6 Graphs over Time
Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
4.6.1 England
4.6.2 Northern Ireland
4.6.3 Scotland
4.6.4 Wales
5 Results by Region
5.1 Cases
Below we daily case count is plotted on a log scale by region:
Daily Cases by Region (7-day moving average)
5.2 Deaths
Below a 7-day moving average of daily deaths by region is plotted on a log scale:
Daily Deaths by Region (7-day moving average)
5.3 Current \(R_{t,m}\) estimates by Region
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Region | Estimate Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Northern Ireland | cases | 93.4 | 2021-05-01 | 0.9 | 1.0 | 1.1 |
| Northern Ireland | deaths | 0.6 | 2021-05-01 | 0.2 | 0.7 | 1.5 |
| Scotland | cases | 167.0 | 2021-05-01 | 0.8 | 0.9 | 0.9 |
| Scotland | deaths | 0.7 | 2021-05-01 | 0.3 | 0.7 | 1.4 |
| Wales | cases | 45.1 | 2021-05-01 | 0.8 | 0.9 | 1.0 |
| Wales | deaths | 0.3 | 2021-05-01 | 0.1 | 0.5 | 1.3 |
| North East | cases | 88.4 | 2021-05-01 | 0.9 | 1.0 | 1.1 |
| North East | deaths | 0.3 | 2021-05-01 | 0.3 | 1.4 | 3.4 |
| North West | cases | 280.1 | 2021-05-01 | 1.0 | 1.1 | 1.1 |
| North West | deaths | 1.0 | 2021-05-01 | 0.2 | 0.5 | 1.0 |
| Yorkshire and The Humber | cases | 348.3 | 2021-05-01 | 0.9 | 1.0 | 1.0 |
| Yorkshire and The Humber | deaths | 1.0 | 2021-05-01 | 0.2 | 0.5 | 0.9 |
| East Midlands | cases | 160.7 | 2021-05-01 | 0.9 | 0.9 | 1.0 |
| East Midlands | deaths | 0.6 | 2021-05-01 | 0.1 | 0.4 | 0.9 |
| West Midlands | cases | 171.4 | 2021-05-01 | 0.9 | 0.9 | 1.0 |
| West Midlands | deaths | 1.0 | 2021-05-01 | 0.3 | 0.7 | 1.3 |
| East of England | cases | 169.0 | 2021-05-01 | 0.9 | 0.9 | 1.0 |
| East of England | deaths | 1.7 | 2021-05-01 | 0.6 | 1.1 | 1.8 |
| London | cases | 250.1 | 2021-05-01 | 0.8 | 0.9 | 0.9 |
| London | deaths | 1.4 | 2021-05-01 | 0.7 | 1.4 | 2.3 |
| South East | cases | 214.9 | 2021-05-01 | 0.9 | 0.9 | 1.0 |
| South East | deaths | 0.4 | 2021-05-01 | 0.2 | 0.6 | 1.4 |
| South West | cases | 107.3 | 2021-05-01 | 0.8 | 0.9 | 1.0 |
| South West | deaths | 1.3 | 2021-05-01 | 0.4 | 0.9 | 1.5 |
Estimated Effective Reproduction Number by Region
5.4 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [5].
5.4.1 Cases
5.4.2 Deaths
5.5 Graphs over Time
Below we plot results for each nation.
5.5.1 Northern Ireland
5.5.2 Scotland
5.5.3 Wales
5.5.4 North East
5.5.5 North West
5.5.6 Yorkshire and The Humber
5.5.7 East Midlands
5.5.8 West Midlands
5.5.9 East of England
5.5.10 London
5.5.11 South East
5.5.12 South West
6 Results by NHS Region
6.1 Current \(R_{t,m}\) estimates by Region
Below current (last weekly) \(R_{t,m}\) estimates are tabulated.
| Region | Estimate Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Northern Ireland | admissions | 4.9 | 2021-05-01 | 0.6 | 0.9 | 1.2 |
| Scotland | admissions | 8.0 | 2021-05-01 | 0.6 | 0.8 | 1.0 |
| Wales | admissions | 14.1 | 2021-05-01 | 0.7 | 0.9 | 1.1 |
| North West | admissions | 13.0 | 2021-05-01 | 0.7 | 0.9 | 1.1 |
| East of England | admissions | 11.7 | 2021-05-01 | 0.6 | 0.8 | 1.0 |
| London | admissions | 14.7 | 2021-05-01 | 0.7 | 0.9 | 1.1 |
| South East | admissions | 8.0 | 2021-05-01 | 0.5 | 0.7 | 0.8 |
| South West | admissions | 5.6 | 2021-05-01 | 0.5 | 0.8 | 1.0 |
| Midlands | admissions | 23.3 | 2021-05-01 | 0.8 | 1.0 | 1.1 |
| North East and Yorkshire | admissions | 18.3 | 2021-05-01 | 0.7 | 0.9 | 1.0 |
Estimated Effective Reproduction Number by Region
6.2 Maps of Effective Reproduction Number
Below we plot the current effective reproduction number on maps with boundaries provided by [6].
6.3 Graphs over Time
Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.
6.3.1 London
6.3.2 South East
6.3.3 South West
6.3.4 East of England
6.3.5 Midlands
6.3.6 North East and Yorkshire
6.3.7 North West
7 Results by Upper Tier Local Authority
7.1 Highest \(R_{t,m}\) as estimated using cases
Below we plot Upper Tier Local Authorities with the highest reproduction numbers (providing they had at least 10 cases per day in last 7 days):
## Selecting by Rt_ui_95| Upper Tier Local Authority | Estimate Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Moray | cases | 10.9 | 2021-05-01 | 1.3 | 1.6 | 2.1 |
| Bolton | cases | 34.4 | 2021-05-01 | 1.3 | 1.5 | 1.8 |
| Newcastle upon Tyne | cases | 18.7 | 2021-05-01 | 1.1 | 1.3 | 1.6 |
| Derry City and Strabane | cases | 20.6 | 2021-05-01 | 1.1 | 1.3 | 1.6 |
| Calderdale | cases | 10.7 | 2021-05-01 | 1.0 | 1.3 | 1.6 |
| Sefton | cases | 10.1 | 2021-05-01 | 1.0 | 1.3 | 1.6 |
| Blackburn with Darwen | cases | 11.4 | 2021-05-01 | 1.0 | 1.2 | 1.6 |
| Kingston upon Hull, City of | cases | 14.4 | 2021-05-01 | 1.0 | 1.2 | 1.5 |
| Cheshire East | cases | 12.1 | 2021-05-01 | 1.0 | 1.2 | 1.5 |
| Trafford | cases | 16.3 | 2021-05-01 | 1.0 | 1.2 | 1.4 |
| Lancashire | cases | 55.4 | 2021-05-01 | 1.0 | 1.2 | 1.3 |
| Lincolnshire | cases | 29.6 | 2021-05-01 | 1.0 | 1.1 | 1.3 |
| Barnsley | cases | 22.3 | 2021-05-01 | 0.9 | 1.1 | 1.3 |
| Rochdale | cases | 11.3 | 2021-05-01 | 0.9 | 1.1 | 1.3 |
| Walsall | cases | 10.1 | 2021-05-01 | 0.9 | 1.1 | 1.4 |
| Oxfordshire | cases | 19.6 | 2021-05-01 | 0.9 | 1.1 | 1.3 |
| Croydon | cases | 10.6 | 2021-05-01 | 0.9 | 1.1 | 1.4 |
| Sheffield | cases | 39.1 | 2021-05-01 | 0.9 | 1.1 | 1.2 |
| Peterborough | cases | 14.6 | 2021-05-01 | 0.9 | 1.1 | 1.3 |
| Swindon | cases | 10.9 | 2021-04-30 | 0.8 | 1.1 | 1.3 |
| Derbyshire | cases | 20.0 | 2021-05-01 | 0.9 | 1.1 | 1.2 |
| Wigan | cases | 10.6 | 2021-05-01 | 0.8 | 1.0 | 1.3 |
| Devon | cases | 15.6 | 2021-05-01 | 0.9 | 1.0 | 1.2 |
| Somerset | cases | 11.3 | 2021-05-01 | 0.8 | 1.0 | 1.3 |
| Slough | cases | 10.7 | 2021-05-01 | 0.8 | 1.0 | 1.2 |
7.2 Risk Quadrants
The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify upper tier local authorities with high cases and high reproduction numbers, or high cases and low reproduction numbers etc.
Values where the reproduction number exceeds 3 are plotted at 3.
7.2.1 Cases
Risk Quadrants - Cases
7.2.2 Deaths
Risk Quadrants - Deaths
7.3 Map of Effective Reproduction Number (Cases)
Below we plot the current effective reproduction number estimated from case data on maps with boundaries provided by [7].
7.4 Map of Reproduction Number by Upper Tier Local Authority Over 60 days
Below the reproduction number by week for each Upper Tier Local Authority is animated over last 60 days:
8 Detailed Results
Detailed output are saved to a comma-separated value file. The file can be found here.
9 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed generation interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection, more so in the case of the use of deaths.
- It’s sensitive to changes in case (or death) detection.
- The generation interval may change over time.
Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.
Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
11 Digital boundaries
Office for National Statistics licensed under the Open Government Licence v.3.0
Contains OS data © Crown copyright and database right 2020
References
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] Office for National Statistics, “Official UK Coronavirus Dashboard,” 2020. [Online]. Available: https://coronavirus.data.gov.uk. [Accessed: 07-Nov-2020]
[4] Office for National Statistics, “Countries (December 2019) Boundaries UK BUC,” 09-Oct-2017. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]
[5] Office for National Statistics, “NUTS Level 1 (January 2018) Ultra Generalised Clipped Boundaries in the United Kingdom,” 31-Jul-2017. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/nuts-level-1-january-2018-ultra-generalised-clipped-boundaries-in-the-united-kingdom. [Accessed: 07-Nov-2020]
[6] Office for National Statistics, “NHS England Regions (April 2020) Boundaries EN BUC,” 13-May-2020. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]
[7] Office for National Statistics, “Counties and Unitary Authorities (December 2019) Boundaries UK BUC,” 11-Mar-2020. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/counties-and-unitary-authorities-december-2019-boundaries-uk-buc. [Accessed: 07-Nov-2020]